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Simplifying 1 = 15x + -1.86x2 Solving 1 = 15x + -1.86x2 Solving for variable 'x'. Reorder the terms: 1 + -15x + 1.86x2 = 15x + -15x + -1.86x2 + 1.86x2 Combine like terms: 15x + -15x = 0 1 + -15x + 1.86x2 = 0 + -1.86x2 + 1.86x2 1 + -15x + 1.86x2 = -1.86x2 + 1.86x2 Combine like terms: -1.86x2 + 1.86x2 = 0.00 1 + -15x + 1.86x2 = 0.00 Begin completing the square. Divide all terms by 1.86 the coefficient of the squared term: Divide each side by '1.86'. 0.5376344086 + -8.064516129x + x2 = 0 Move the constant term to the right: Add '-0.5376344086' to each side of the equation. 0.5376344086 + -8.064516129x + -0.5376344086 + x2 = 0 + -0.5376344086 Reorder the terms: 0.5376344086 + -0.5376344086 + -8.064516129x + x2 = 0 + -0.5376344086 Combine like terms: 0.5376344086 + -0.5376344086 = 0.0000000000 0.0000000000 + -8.064516129x + x2 = 0 + -0.5376344086 -8.064516129x + x2 = 0 + -0.5376344086 Combine like terms: 0 + -0.5376344086 = -0.5376344086 -8.064516129x + x2 = -0.5376344086 The x term is -8.064516129x. Take half its coefficient (-4.032258065). Square it (16.25910510) and add it to both sides. Add '16.25910510' to each side of the equation. -8.064516129x + 16.25910510 + x2 = -0.5376344086 + 16.25910510 Reorder the terms: 16.25910510 + -8.064516129x + x2 = -0.5376344086 + 16.25910510 Combine like terms: -0.5376344086 + 16.25910510 = 15.7214706914 16.25910510 + -8.064516129x + x2 = 15.7214706914 Factor a perfect square on the left side: (x + -4.032258065)(x + -4.032258065) = 15.7214706914 Calculate the square root of the right side: 3.965030982 Break this problem into two subproblems by setting (x + -4.032258065) equal to 3.965030982 and -3.965030982.Subproblem 1
x + -4.032258065 = 3.965030982 Simplifying x + -4.032258065 = 3.965030982 Reorder the terms: -4.032258065 + x = 3.965030982 Solving -4.032258065 + x = 3.965030982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + x = 3.965030982 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + x = 3.965030982 + 4.032258065 x = 3.965030982 + 4.032258065 Combine like terms: 3.965030982 + 4.032258065 = 7.997289047 x = 7.997289047 Simplifying x = 7.997289047Subproblem 2
x + -4.032258065 = -3.965030982 Simplifying x + -4.032258065 = -3.965030982 Reorder the terms: -4.032258065 + x = -3.965030982 Solving -4.032258065 + x = -3.965030982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + x = -3.965030982 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + x = -3.965030982 + 4.032258065 x = -3.965030982 + 4.032258065 Combine like terms: -3.965030982 + 4.032258065 = 0.067227083 x = 0.067227083 Simplifying x = 0.067227083Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.997289047, 0.067227083}
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